Electronic – Grouping Components in Eagle

No, you don't want to show multiple connections for the same physical pin on the schematic. This will lead to confusion because anyone else looking at the schematic will expect that each of those connections is actually a different physical pin.

You do this by listing all the possible pin functions in the pin name. For example, here is what my PIC 18F67J60 part looks like in a schematic:

First notice that power pins are at top and ground pins at bottom. That reduces some of the clutter around the remaining pins, and of course makes the schematic more clear on its own. In most cases, a circuit will only make use of one of the functions of each pin. It would be nice if there was a way to highlight the function or functions actually used, but removing the unused functions is worse. It can be quite useful to see what the part could have done or might do with different firmware.

Most of the time how a pin gets used is obvious from the schematic. One trick that greatly helps with this is to show logical direction for pins. I have little arrow symbols in Eagle just for that purpose. They are small and therefore don't get in the way, but help a great deal towards clarifying the circuit. Reasonable net names also help. Here is a small section of a schematic with the direction arrows and net names:

Particularly note the bottom two pins. Those are UART signals to another processor, so thereby are using the TX and RX functions of those pins. Each net can only have a single name, even though it will be the TX function (output) on one processor and the RX function (input) on the other. In this case I named the nets from this processor's point of view. This is the network processor within the overall device, so I named them NETTX and NETRX to help indicate the names are relative to this processor. However, there is potential for confusion at the other processor since NETTX will go into its RX pin and NETRX will go out of its TX pin. The arrows at the other processor will help a lot to head off a likely confusion.

Why were these packages designed this way?

I can't say for sure why you have the very tiny label on that particular part. Perhaps the idea was to make it "disappear" without deleting it altogether. This allows it to still appear on a BOM, for example.

In general, the value field is not normally used in the silkscreen at all, except maybe in certain educational projects or kits.

Normally, the value field is used only in an assembly drawing, where it just needs to be small enough to match the general size of the part on the drawing.

What is the best way to fix the errors caused by these labels?

As I said above, simply don't include the value field in your silkscreen layer. This is why "names" and "values" have their own layers in the design stack.

Otherwise, it would probably be worth your while to create a custom library that has the labels the way you want them.